1. In a small saucepan, combine the cranberries, granulated sugar, orange juice, orange zest, and cinnamon stick. Bring to a simmer over medium heat and cook for 10–12 minutes, stirring occasionally, until the cranberries burst and the sauce thickens. Remove the cinnamon stick and let the sauce cool completely.

2. Preheat the oven to 400°F (200°C).

3. In a large bowl, combine the sliced Granny Smith and Honeycrisp apples with the brown sugar, granulated sugar, flour, cinnamon, nutmeg, cornstarch, salt, and vanilla extract. Toss until evenly coated.

4. Fit the pie crust into a 9-inch pie plate. Spoon half of the apple mixture into the crust.

5. Spread the cooled cranberry sauce evenly over the apples, then top with the remaining apple mixture. Dot the top with the butter cubes.

6. Arrange the remaining pie crust (or lattice strips if using a double crust) over the filling. Crimp and seal the edges, then brush the top with the beaten egg.

7. Bake for 20 minutes at 400°F (200°C), then reduce the oven temperature to 375°F (190°C) and continue baking for 50–55 minutes, until the crust is golden brown and the filling is bubbling.

8. If the crust browns too quickly, loosely cover the edges with foil during the final 20–30 minutes of baking.

9. Cool the pie for at least 3 hours before slicing to allow the filling to set.